Related papers: Group representation design of digital signals and…
We report an implementation of self-consistent Green's function many-body theory within a second-order approximation (GF2) for application with molecular systems. This is done by iterative solution of the Dyson equation expressed in matrix…
A system of ${N_{osc}}$ charged oscillators interacting with the electromagnetic field, spatially confined in a 3D lattice of sub-wavelength dimension, can condense into a superradiant coherent state if appropriate density and frequency…
This article is devoted to the investigation of semidirect products of groups of loops and groups of diffeomorphisms of finite and infinte dimensional real, complex and quaternion manifolds. Necessary statements about quaternion manifolds…
Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier…
It is demonstrated is this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithms with higher orders of convergence. Excluding the cost of…
We investigate the theory of affine groups in the context of designing radar waveforms that obey the desired wideband ambiguity function (WAF). The WAF is obtained by correlating the signal with its time-dilated, Doppler-shifted, and…
Motivated by the aim to find new medical strategies to suppress undesirable neural synchronization we study the control of oscillations in a system of inhibitory coupled noisy oscillators. Using dynamical properties of inhibition, we find…
We have developed a linearization method to investigate the subthreshold oscillatory behaviors in nonlinear autonomous systems. By considering firstly the neuronal system as an example, we show that this theoretical approach can predict…
We demonstrate the utility of machine learning algorithms for the design of Oscillatory Neural Networks (ONNs). After constructing a circuit model of the oscillators in a machine-learning-enabled simulator and performing Backpropagation…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
We develop a functorial theory of spinor and oscillator representations parallel to the theory of Schur functors for general linear groups. This continues our work on developing orthogonal and symplectic analogues of Schur functors. As…
Networks of coupled degrade-and-fire (DF) oscillators are simple dynamical models of assemblies of interacting self-repressing genes. For mean-field interactions, which most mathematical studies have assumed so far, every trajectory must…
Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for…
Given a real closed polytope $P$, we first describe the Fourier transform of its indicator function by using iterations of Stokes' theorem. We then use the ensuing Fourier transform formulations, together with the Poisson summation formula,…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
In this paper, we introduce a new function related to the sum of element orders of finite groups. It is used to give some criteria for a finite group to be cyclic, abelian, nilpotent, supersolvable and solvable, respectively.
Integrated Sensing and Communications (ISAC) has garnered significant attention as a promising technology for next-generation wireless and vehicular communications. Among candidate waveforms, Orthogonal Frequency Division Multiplexing…
We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate…
We describe and demonstrate a new oscillator topology, the parametric feedback oscillator (PFO). The PFO paradigm is applicable to a wide variety of nanoscale devices, and opens the possibility of new classes of oscillators employing…
Networks of coupled nonlinear oscillators model a broad class of physical, chemical and biological systems. Understanding emergent patterns in such networks is an ongoing effort with profound implications for different fields. In this work,…